RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions

Abstract

The present application belongs to the field of multi-scale modeling of composite materials, and is a RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions. The method first establishes a basic analysis model of composite materials, generates a number of randomly distributed particle coordinates in the RVE region of the RVE basic model of composite materials through random commands, and then respectively judges whether the particles are in the RVE region, whether the particles overlap, whether the particles overlap with the model boundary, and the volume percentage, so as to determine the coordinates of each particle and its derivative particles that meet the generation requirements, and then generates a txt format file, generates a finite element model through finite element analysis software and performs finite element analysis, so as to calculate the effective mechanical properties of the composite material. It is possible to generate completely random particles and their derivative particles that meet the needs of finite element analysis, and at the same time, it is not necessary to avoid contact with the RVE boundary, and the periodic boundary conditions are convenient to apply, so that the effective mechanical properties of composite materials with random particle distribution can be accurately predicted.

Description

Technical Field

[0001] The present application belongs to the field of multi-scale modeling of composite materials, and in particular relates to a RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions. Background Art

[0002] The steps of effective mechanical properties analysis of composite materials based on numerical analysis can generally be divided into: representative volume element modeling, periodic boundary condition loading, and effective mechanical properties calculation. Among them, the representative volume element (RVE) is an important representation form of the microscopic configuration of the composite material. Its modeling is the basis of mechanical analysis. According to the location of its reinforcement phase, typical RVEs include body-centered, face-centered, edge-centered, and random distribution models. In the actual composite molding process, the particles and fibers are randomly distributed inside the composite material, and its effective mechanical properties are closely related to the distribution form of the reinforcement phase. Therefore, random distribution is the main distribution form of particle reinforcement phase and fiber reinforcement phase inside the composite material, which can reflect the microstructure of the composite material and is used by most numerical simulation methods; periodic boundary conditions are used to reflect the mutual influence between adjacent RVEs inside the composite material. For example, the contact surface of two adjacent RVEs needs to ensure that the displacement is exactly the same. However, based on the characteristics of RVE, the two adjacent RVEs are actually the same structure. Therefore, the displacement of RVE relative to three groups of symmetry planes, three groups of edges, and eight vertices is the same. The above requirements bring difficulties to the application of periodic boundary conditions of randomly distributed RVE.

[0003] The main reason for the difficulty in RVE modeling of randomly distributed particle composites is that it is necessary to consider the application of periodic boundary conditions during the modeling process. When the particle reinforcement phase is cut by the RVE surface, edge, or vertex, its remaining part needs to appear on the corresponding surface, edge, or vertex. At the same time, when the model is meshed, it is necessary to ensure that there are paired nodes at the corresponding positions to satisfy the application of periodic boundary conditions.

[0004] At present, there are three main means to solve the above problems:

[0005] (1) Avoid contact between the reinforcement phase and the RVE boundary

[0006] A method for predicting the macroscopic effective properties of composite materials with randomly distributed particles is proposed. The position of the particle reinforcement phase is controlled so that it does not contact the RVE boundary. In the grid division, the boundary layer is entirely matrix phase, which can ensure the existence of paired nodes at corresponding positions. However, the above method cannot characterize the particles at the RVE boundary, resulting in the inability to model composite materials with large particle volume percentages, which has limitations.

[0007] (2) Limited random distribution method

[0008] Before establishing the random distribution model, a uniform distribution RVE is first established according to the geometric configuration and volume percentage of the reinforcement phase, and then random perturbations are applied to each particle or fiber to change its position, and finally periodic boundary conditions are applied to the model. In the prior art, a random structure generation method for unidirectional fiber composite materials is used. The random distribution model constructed based on the above means is still improved on the basis of the uniform model, and it is difficult to achieve complete randomness.

[0009] (3) Random distribution model based on intelligent algorithm

[0010] A method for generating random structures of long fiber composite materials and predicting their elastic properties in the prior art realizes modeling of randomly distributed fiber composite materials through a particle swarm algorithm combined with corresponding objective functions and control equations. The above method is aimed at fiber-reinforced composite materials, and only needs to construct a two-dimensional randomly distributed structure, and three-dimensional model construction is realized by stretching. In addition, the fiber-reinforced phase can be divided into hexahedrons, which makes it easier to apply periodic boundary conditions. However, the particle-reinforced phase needs to construct a three-dimensional randomly distributed structure, and the particle-reinforced phase grid is a tetrahedron, which increases the difficulty of modeling and applying periodic boundary conditions.

[0011] To this end, the present invention develops a composite RVE modeling method that considers a completely random particle reinforcement phase that can be applied at the PVE boundary. Summary of the invention

[0012] The purpose of this application is to provide an RVE modeling method for composite materials with random particle distribution taking into account periodic boundary conditions, so as to solve the problem in the prior art that it is difficult to apply the particle reinforcement phase completely randomly or difficult to perform RVE modeling at the RVE boundary.

[0013] The technical solution of the present application is: a RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions, comprising:

[0014] Determine the model input parameters, establish the composite material basic analysis model, and generate a number of randomly distributed particle coordinates in the RVE region of the composite material RVE basic model through random commands;

[0015] Each time a new particle is randomly generated, a check is performed to determine whether the particle is within the RVE area. If so, the next step is executed; if not, the particle is deleted.

[0016] Determine whether the new particle overlaps with the previous particle and its derivative particles. If so, delete the particle; if not, execute the next step;

[0017] Determine whether the new particle coincides with the model boundary. If so, generate a derivative particle at the corresponding position according to the coincident position; if not, execute the next step;

[0018] Determine whether the volume percentage of the new particle meets the requirements. If so, generate the particle. If not, delete the particle. Determine again whether the number of particles meets the requirements. If so, stop generating new particles and establish the final analysis model of the composite material. If not, generate new particles again.

[0019] Obtain the coordinate values ​​of each particle and its derived particles in the final RVE model of the composite material, generate a txt format file, input the txt format file into the finite element analysis software, delete all particle entity parts beyond the matrix, and generate a randomly distributed particle finite element model;

[0020] Assign model attributes, periodic boundary conditions, and load types, and perform finite element analysis. Volume averaging is performed based on the results of the finite element model of randomly distributed particles to calculate the effective mechanical properties of the composite material.

[0021] Preferably, the method for randomly generating particles in the composite material RVE basic model by random commands is:

[0022] Assume that the center of one particle is the origin of the coordinate system, namely O1(0, 0, 0), the center coordinates of the other particle are O2(x2, y2, z2), the distance between O1 and O2 is l, and the two polar angles are denoted as θ and O2(x2, y2, z2) can be obtained by l, θ and express:

[0023]

[0024]

[0025]

[0026] Let l, θ and Randomly select values ​​within its feasible domain, that is, i = rand (l min , l max ),θ=rand(0,π), Wherein a=rand(b,c) means that a takes a random value in the range of b to c.

[0027] Preferably, the method for determining whether a new particle overlaps with a previous particle and its derivative particles is:

[0028] Determine whether the particles overlap to satisfy the following formula:

[0029] (x i -x k ) 2 +(y i -y k )2 +(z i -z k ) 2 ≤l min 2

[0030] Determine whether the derived particles overlap to satisfy the following formula:

[0031]

[0032] Where k is any integer between (1, i-1), l min is the minimum spacing between particles, j and l are the number of derived particles of the i-th and k-th times respectively. If both are satisfied, the new particles will not overlap with the previous particles; if any of the above items is not satisfied, the new particles will overlap with the previous particles.

[0033] Preferably, the method for determining whether a new particle is within the RVE region is:

[0034] Assume that the size boundaries of the composite material foundation analysis model are X∈(-L x , L x ), Y∈(-L y , L y ), Z∈(-L z , L z ), the particle radius is r, and the center coordinates of the i-th particle are O i (x i ,y i , z i );

[0035] Determine whether x is satisfied at the same time i ∈(-L x , L x ), y i ∈(-L y , L y ), z i ∈(-L z , L z ) or |x i |∈(L x , L x +r) or |y i |∈(L y , L y +r) or |z i |∈(L z , L z +r), O i The distance to the nearest face, edge or vertex is less than r;

[0036] If the above requirements are met, it is determined that the new particle is in the RVE area; if the above requirements are not met, it is determined that the new particle is not in the RVE area.

[0037] Preferably, when a new particle coincides with the model boundary, further judgment is made as follows: when a particle coincides with only a certain face of RVE, its derivative particles are generated near the corresponding face; when a particle coincides with only a certain edge of RVE, its derivative particles are generated near the other three corresponding edges; when a particle coincides with a certain vertex of RVE, its derivative particles are generated near the remaining seven vertices.

[0038] Preferably, MATLAB is used to construct a basic analysis model of the composite material, and ANSYS is used to perform finite element analysis of the particles and their derivative particles.

[0039] The present invention discloses a RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions, which first establishes a composite material basic analysis model, generates a number of randomly distributed particle coordinates in the RVE region of the composite material RVE basic model through random commands, and then respectively judges whether the particles are in the RVE region, whether the particles overlap, whether the particles overlap with the model boundary, and the volume percentage, so as to determine the coordinates of each particle and its derivative particles that meet the generation requirements, and then generates a txt format file, generates a finite element model through finite element analysis software and performs finite element analysis, so as to calculate the effective mechanical properties of the composite material. It is possible to generate completely random particles and their derivative particles that meet the requirements of finite element analysis, and at the same time, it is not necessary to avoid contact with the RVE boundary, the modeling difficulty is low, and the periodic boundary conditions are easy to apply, so that the effective mechanical properties of composite materials with random particle distribution can be accurately predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0041] Figure 1 It is the overall idea diagram of modeling of the present invention;

[0042] Figure 2 Modeling flow chart for the present invention;

[0043] Figure 3 The i+1th particle schematic diagram is randomly generated for the present invention;

[0044] Figure 4 This is a schematic diagram of the present invention for determining whether a particle is inside the RVE;

[0045] Figure 5 A schematic diagram of the method for generating derivative particles of the present invention;

[0046] Figure 6 This is a schematic diagram of the center coordinates of the particles of the present invention and their derivative particles in a txt file;

[0047] Figure 7 This is a schematic diagram of the spatial position of randomly distributed particles and ANSYS modeling of the present invention;

[0048] Figure 8 Schematic diagram of RVE of a composite material with random distribution of particles considering periodic boundary conditions in the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] A RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions, such as Figure 1 As shown, the geometric information is input through MATLAB to construct the basic analysis model of the composite material, so as to output the center coordinate value of the particle; then the material information is input into ANSYS to perform finite element analysis of the particles and their derivative particles, and generate a finite element model of randomly distributed particles.

[0051] Of course, actual model construction is not limited to MATLAB software, and finite element analysis software is not limited to ANSYS software. This embodiment only uses MATLAB software and ANSYS software to illustrate composite material RVE modeling in one case.

[0052] like Figure 2 As shown, the specific steps include:

[0053] Step S100, determine the model input parameters, including model size, particle / fiber radius, interface micro thickness, volume percentage, number of particles, minimum particle spacing and other geometric information, establish a basic analysis model of composite materials, and generate a number of randomly distributed particle coordinates or fiber center position coordinates in the RVE area of ​​the composite material RVE basic model through random commands.

[0054] The premise for generating randomly distributed particles is that each RVE region and the particles inside are exactly the same. The following is only an explanation of one RVE region, and the other RVE regions can be arranged in an array. The RVE region used in this application is a cube structure.

[0055] Taking particle reinforced composite materials as an example, the position relationship between two adjacent particles is as follows: Figure 3 As shown:

[0056] In order to avoid loss of generality, assume that the center of one particle is the origin of the coordinate system, namely O1(0, 0, 0), the coordinates of the center of the other particle are O2(x2, y2, z2), the distance between O1 and O2 is l, and the two polar angles are denoted as θ and O2(x2, y2, z2) can be obtained by l, θ and express:

[0057]

[0058] To ensure the randomness of particle distribution, let l, θ and Randomly select values ​​within its feasible domain, that is, l = rand (l min , l max ),θ=rand(0,π), Wherein a=rand(b,c) means that a takes a random value in the range of b to c.

[0059] Therefore, any two adjacent particles O i (x i ,y i , z i ) and O i+1 (x i+1 ,y i+1 , z i+1 ) have the following relationship

[0060]

[0061] Spherical particles can be formed by formulas (1) and (2), but the shape of particles that can be generated in practice is not limited to spheres, and can be ellipsoids or quasi-spheres, etc. Generating spherical particles is only one implementation method of this embodiment.

[0062] For fiber-reinforced composites, circles are randomly generated perpendicular to the fiber cross section, and the process is similar to the above method.

[0063] In step S200, since the generated particle coordinates are completely random and the range of the RVE area is generally a cubic structure, the generated particles may overlap, be located outside the RVE area, or exceed the boundary of the RVE model. However, such situations do not exist for the actual RVE area, so they need to be eliminated one by one.

[0064] That is to say, in the generated composite material analysis model, the boundary restrictions and symmetry conditions of the reinforcement phase need to be considered, and the obtained random distribution model is required to meet the following requirements:

[0065] (1) At least part of the particle must be inside the analysis model;

[0066] (2) Composite material analysis models need to be continuous on boundaries.

[0067] Each time a new particle is randomly generated, that is, particle i+1, a determination is made as to whether the particle is in the RVE area. If so, the next step is executed; if not, the particle is deleted;

[0068] For particles randomly generated outside the RVE area, the above requirement (1) is not met and they can be deleted directly.

[0069] The method for judging whether a new particle is in the RVE area is as follows:

[0070] Assume that the size boundaries of the composite material foundation analysis model are X∈(-L x , L x ), Y∈(-L y , L y ), Z∈(-L z , ,L z ), the particle radius is r, and the center coordinates of the i-th particle are O i (x i ,y i , z i );

[0071] When x i ∈(-L x , L x ), y i ∈(-L y , L y ), z i ∈(-L z , L z ), requirement (1) must be satisfied;

[0072] When |x i |∈(L x , L x +r) or |y i |∈(L y , L y +r) or |z i |∈(L z , L z +r), O i The distance to the nearest face, edge or vertex must be less than r to meet requirement (1).

[0073] Therefore, if the above requirements are met, it is determined that the new particle is in the RVE area; if the above requirements are not met, it is determined that the new particle is not in the RVE area.

[0074] Therefore, with O iThe particle at the center of the circle meets the requirement (1) as follows Figure 4 As shown, O i Inside the dotted line in the figure.

[0075] Step S300, determining whether the new particle overlaps with the previous particle and its derivative particles, if so, deleting the particle; if not, executing the next step.

[0076] Preferably, whether the new particle overlaps with the previous particle and its derivative particles is judged by the distance difference between the centers of the two particles, and the method is:

[0077] Determine whether the particles overlap and whether they satisfy the following formula:

[0078] (x i -x k ) 2 +(y i -y k ) 2 +(z i -z k ) 2 ≤l min 2 (3)

[0079] Determine whether the derived particles satisfy the following formula:

[0080]

[0081] Where k is any integer between (1, i-1), l min is the minimum spacing between particles, j and l are the number of derived particles of the i-th and k-th times respectively. If both are satisfied, the new particles will not overlap with the previous particles; if any of the above items is not satisfied, the new particles will overlap with the previous particles.

[0082] By comparing the distance between the center coordinates of adjacent particles with the minimum spacing between particles, it is possible to accurately determine whether there is overlap between particles.

[0083] Step S400: Whether the model boundaries overlap is closely related to the boundary continuity in requirement (2).

[0084] In order to satisfy the continuity of the analysis model on the boundary, it is necessary to segment the particles that intersect with the faces, edges and vertices, and place the segmented parts on the corresponding symmetrical faces, edges and vertices, such as Figure 5 shown.

[0085] As we know, in order to satisfy the boundary continuity condition, new particles will be derived. Therefore, in the i-th randomly generated O i The coordinates of the particle centers derived from them are shown in Table 1.

[0086] Table 1 Coordinate values ​​of particle centers satisfying boundary continuity

[0087]

[0088]

[0089] in, The subscript i in represents the i-th particle generated by a random method, and the superscript k represents the k-th new particle derived when a particle intersects the model boundary.

[0090] Determine whether the new particle coincides with the model boundary. If so, generate a derivative particle at the corresponding position according to the coincident position; if not, execute the next step.

[0091] To determine whether a particle coincides with the model boundary, it is necessary to determine the distance between the particle center point and the model boundary vertex, the minimum distance between the particle center point and the model edge, and the minimum distance between the particle center point and the corresponding surface of the model. If it is less than the radius of the particle, it is determined that there is an overlap. Different derivative particles will not be generated based on the repositioning, thereby effectively ensuring the continuity of the model boundary.

[0092] When a particle coincides with only one face of RVE, its derivative particles are generated near the corresponding face; when a particle coincides with only one edge of RVE, its derivative particles are generated near the other three corresponding edges; when a particle coincides with a vertex of RVE, its derivative particles are generated near the remaining seven vertices.

[0093] In a specific embodiment, taking a particle-reinforced composite material as an example, Table 2 shows the RVE parameters of a particle randomly distributed composite material.

[0094] Table 2 Random distribution particle size parameters

[0095]

[0096] The center coordinates of random particles with a certain volume percentage are calculated by programming with MATLAB software. Taking vol=29.26% as an example, 9 complete particles are required for calculation by MATLAB. The coordinates of the sphere center of each particle are shown in Table 3. There are 19 particle coordinates in the table, which are the center coordinates of 9 complete particles and their derived particles.

[0097] Table 3 Coordinate values ​​of particle center under the condition of vol=29.26%

[0098]

[0099] Step S500, the volume percentage reflects the density of the particles in the RVE area. Only when the density reaches the set value, the material generated by the particles can meet the use requirements. The specific judgment method is: judge whether the volume percentage of the new particles meets the requirements. If so, generate the particles, if not, delete the particles; judge again whether the number of particles meets the requirements. If so, stop generating new particles and form a final analysis model for the composite material. If not, generate new particles again. The particle density in the RVE area takes the volume percentage as the final reference standard. When the particle density meets the requirements, no new particles will be generated.

[0100] While new particles are being generated, the number of old particles that have been generated needs to be continuously counted. When the number of old particles reaches the upper limit, no new particles will be generated.

[0101] When a newly generated particle exceeds the PVE area and overlaps with the original particle and its derivative particles, the newly generated particle is deleted and a search count is performed. Finally, all search results are archived and it is determined whether all particles in this round are searched successfully. If so, the generation of all particles is completed.

[0102] Through the above steps, the generation of completely random particles and their derived particles is achieved. Through the design of derived particles, the contact with the RVE boundary is achieved while ensuring the continuity of the model.

[0103] Step S600, obtaining the coordinate values ​​of each particle and its derivative particles in the final model of the composite material RVE, and representing the above coordinate values ​​in three-dimensional space, such as Figure 6 As shown in the figure, a txt format file is generated, and the txt format file is input into the ANSYS software, all the particle entities beyond the matrix are deleted, and a randomly distributed particle finite element model is generated based on its APDL language. The established model is as follows Figure 7 shown.

[0104] The format file is not limited to the txt format, but can also be in the xml format, etc. The input of the format file can be freely selected. The means by which ANSYS software generates particles according to coordinates is a conventional means, and the details will not be repeated.

[0105] After the random distribution particle finite element model is generated, the tetrahedral mesh is used for meshing, such as Figure 8 As shown, each discretized interface layer contains a layer of tetrahedral units to facilitate subsequent analysis.

[0106] Step S700, assigning model attributes, periodic boundary conditions, and load types, and performing finite element analysis, performing volume averaging based on the results of the randomly distributed particle finite element model, and calculating the effective mechanical properties of the composite material.

[0107] Preferably, the equivalent elastic modulus E is used. eff and the equivalent shear modulus G eff Indicates its equivalent mechanical properties. In the finite element simulation, the compression and shear process of the material is simulated by applying constraints and loads on different surfaces, as shown in Table 4

[0108] Table 4 Constraints and load conditions for compression and shear conditions

[0109]

[0110] where x - Represents the face of the cube along the negative direction of the x-axis, and X represents the constraint or load along the x-direction. Based on the finite element simulation method, the stress and strain distribution inside the model under the above two loads are solved, and the volume average of the stress and strain is solved to obtain the equivalent elastic modulus of the composite material with random particle distribution. Its equivalent bulk modulus and shear modulus are equal to the ratio of the stress / strain volume average in the corresponding direction, that is:

[0111]

[0112] in and Respectively represent σ ij and ε ij The volume average.

[0113] This application first establishes a basic analysis model for composite materials, generates a number of randomly distributed particle coordinates in the RVE region of the composite material RVE basic model through random commands, and then respectively judges whether the particles are in the RVE region, whether the particles overlap, whether the particles overlap with the model boundary, and the volume percentage, so as to determine the coordinates of each particle and its derivative particles that meet the generation requirements, and then generates a txt format file, generates a finite element model through finite element analysis software and performs finite element analysis, so as to calculate the effective mechanical properties of the composite material. It is possible to generate completely random particles and their derivative particles that meet the needs of finite element analysis, and at the same time, there is no need to avoid contact with the RVE boundary, the modeling difficulty is low, and the periodic boundary conditions are easy to apply, so that the effective mechanical properties of composite materials with random particle distribution can be accurately predicted.

[0114] Finally, a few points should be explained: First, in the description of this application, it should be noted that, unless otherwise specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, which may refer to mechanical connection or electrical connection, or internal communication between two components, or direct connection. "upper", "lower", "left", "right", etc. are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may change;

[0115] Secondly: In the drawings of the embodiments disclosed in the present invention, only the structures related to the embodiments disclosed in the present invention are involved, and other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of the present invention can be combined with each other;

[0116] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions, characterized in that: include: Determine the model input parameters, establish the composite material basic analysis model, and generate a number of randomly distributed particle coordinates in the RVE area of ​​the composite material RVE basic model through random commands; Each time a new particle is randomly generated, a check is performed to determine whether the particle is within the RVE area. If so, the next step is executed; if not, the particle is deleted. Determine whether the new particle overlaps with the previous particle and its derivative particles. If so, delete the particle; if not, execute the next step; Determine whether the new particle coincides with the model boundary. If so, generate a derivative particle at the corresponding position according to the coincident position; if not, execute the next step; Determine whether the volume percentage of the new particle meets the requirements. If so, generate the particle. If not, delete the particle. Determine again whether the number of particles meets the requirements. If so, stop generating new particles and establish the final analysis model of the composite material. If not, generate new particles again. Obtain the coordinate values ​​of each particle and its derived particles in the final RVE model of the composite material, generate a txt format file, input the txt format file into the finite element analysis software, delete all particle entity parts beyond the matrix, and generate a randomly distributed particle finite element model; Assign model attributes, periodic boundary conditions, load types, and perform finite element analysis. Perform volume averaging based on the results of the finite element model of randomly distributed particles to calculate the effective mechanical properties of the composite material. The method for randomly generating particles in the composite material RVE basic model through random commands is: Assume that the center of one particle is the origin of the coordinate system, namely O1(0, 0, 0), the center coordinates of the other particle are O2(x2, y2, z2), the distance between O1 and O2 is l, and the two polar angles are denoted as θ and O2(x2, y2, z2) can be obtained by l, θ and express: Let l, θ and Randomly select values ​​within its feasible domain, that is, l = rand (l min , l max ),θ=rand(0,π), The method for determining whether a new particle overlaps with the previous particle and its derivative particles is as follows: Determine whether the particles overlap to satisfy the following formula: (x i -x k ) 2 +(y i -y k ) 2 +(z i -z k ) 2 ≤l min 2 Determine whether the derived particles overlap to satisfy the following formula: Where k is any integer between (1, i-1), l min is the minimum spacing between particles, j and l are the number of derived particles of the i-th and k-th times respectively. If both are satisfied, the new particles will not overlap with the previous particles; if any of the above items is not satisfied, the new particles will overlap with the previous particles.

2. The RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions according to claim 1, characterized in that: The method for judging whether a new particle is in the RVE area is as follows: Assume that the size boundaries of the composite material foundation analysis model are X∈(-L x , L x ), Y∈(-L y , L y ), Z∈(-L z , L z ), the particle radius is r, and the center coordinates of the i-th particle are O i (x i ,y i , z i ); Determine whether x is satisfied at the same time i ∈(-L x , L x ), y i ∈(-L y , L y ), z i ∈(-L z , L z ) or |x i |∈(L x , ,L x +r) or |y i |∈(L y , L y +r) or |z i |∈(L z , L z +r), O i The distance to the nearest face, edge or vertex is less than r; If the above requirements are met, it is determined that the new particle is in the RVE area; if the above requirements are not met, it is determined that the new particle is not in the RVE area.

3. The RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions as claimed in claim 1, characterized in that: When a new particle coincides with the model boundary, further judgment is made as follows: when a particle coincides with only one face of RVE, its derivative particles are generated near the corresponding face; when a particle coincides with only one edge of RVE, its derivative particles are generated near the other three corresponding edges; when a particle coincides with a vertex of RVE, its derivative particles are generated near the remaining seven vertices.

4. The RVE modeling method for composite materials with random particle distribution considering periodic boundary conditions as claimed in claim 1, characterized in that: MATLAB is used to construct the basic analysis model of composite materials, and ANSYS is used to perform finite element analysis of particles and their derived particles.

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